4 of 4 added 696 characters in body

Pyth, 37 33 29 28 bytes

The code contains an unprintable character, so here is an xxd hexdump.

00000000: 737d 5173 4d5e 733c 5252 6336 2e22 6174  s}QsM^s<RRc6."at
00000010: 14d0 69ba 76f1 ac59 6422 346c            ..i.v..Yd"4l

Try it online.

Extremely Astronomically inefficient. The time and space complexity is O(16n) O(24n).

Explanation

First, a Q is implicitly appended.

s}QsM^s<RRc6."…"4lQ     Implicit: Q = input
            ."…"        Generate "logsincostanlnee"
          c6            Split in 6 parts: ["log", "sin", "cos", "tan", "ln", "ee"]
         R      4       For each n from 0 to 3
       <R               Take the first n chars from each string
      s                 Flatten the results
                 lQ     Get length of input
     ^                  Take that Cartesian power of the list
   sM                   Join each resulting list
 }Q                     Check if the input is found
s                       Cast to integer